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Solve the equation 3sinh(2x) = 13 - 3e^(2x), answering in the form 0.5ln(k). where k is an integer

We know that: sinh(2x) = 2sinh(x)cosh(x) , therefore the equation becomes 6sinh(x)cosh(x) = 13 - 3e^2xWe also know that sinh(x) = 0.5*[e^x-e^-x] and that cosh(x) = 0.5*[e

Answered by Matt H. • Further Mathematics tutor

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Given that y = arcsinh(x), show that y=ln(x+ sqrt(x^2 + 1) )

In questions involving hyperbolic functions and natural logs, it is often useful to rewrite things in terms of e, since then you might be able to take a natural log at the end of your answer. Here, we can...

Answered by Sam B. • Further Mathematics tutor

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Using graphs, show how the Taylor expansion can be used to approximate a trigonometric function.

The Taylor expansion/theorem is used to express any function as a power series about a certain point. Using the given formula of the Taylor expansion, we can approximate a trigonometric function (for exam...

Answered by Matthew T. • Further Mathematics tutor

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Solve for z in the equation sin(z) = 2

Note that |sin(x)| <= 1 for all real x, so our solution must be complex if one exists at all
Euler's formula gives that exp(ix) = cos(x) + isin(x), and hence exp(-ix) = cos(x) - isin(x) since cos ...

Answered by Sam L. • Further Mathematics tutor

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Solve the following inequality: 2x^2 < x+3

2x² < x+3, 2x²- x - 3 < 0, (2x - 3) (x + 1) < 0, Positive quadratic. Roots: x = -1 and x = 3/2, Therefore, x takes values greater than -1 and less tha...

Answered by Olia M. • Further Mathematics tutor

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